7L 3s: Difference between revisions
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'''7L 3s''' | '''7L 3s''' refers to the structure of [[MOSScales|moment of symmetry scales]] built from a 10-tone chain of neutral thirds (assuming a period of an octave): | ||
L s L L L s L L s L | L s L L L s L L s L | ||
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t q t t t q t t q t | t q t t t q t t q t | ||
== Names== | |||
=Interval ranges= | This MOS is called '''dicoid''' (DY-koid; named after the abstract temperament [[dicot]]) in [[TAMNAMS]]. | ||
==Interval ranges== | |||
The generator (g) will fall between 343 cents (2\7 - two degrees of [[7edo|7edo]] and 360 cents (3\10 - three degrees of [[10edo|10edo]]), hence a neutral third. | The generator (g) will fall between 343 cents (2\7 - two degrees of [[7edo|7edo]] and 360 cents (3\10 - three degrees of [[10edo|10edo]]), hence a neutral third. | ||
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The most frequent interval, then is the neutral third (and its inversion, the neutral sixth), followed by the perfect fourth and fifth. Thus, 7+3 combines the familiar sound of perfect fifths and fourths with the unfamiliar sounds of neutral intervals. They are compatible with Arabic and Turkish scales, but not with traditional Western ones. | The most frequent interval, then is the neutral third (and its inversion, the neutral sixth), followed by the perfect fourth and fifth. Thus, 7+3 combines the familiar sound of perfect fifths and fourths with the unfamiliar sounds of neutral intervals. They are compatible with Arabic and Turkish scales, but not with traditional Western ones. | ||
=Scale tree= | ==Scale tree== | ||
The generator range reflects two extremes: one where L=s (3\10), and another where s=0 (2\7). Between these extremes, there is an infinite continuum of possible generator sizes. By taking freshman sums of the two edges (adding the numerators, then adding the denominators), we can fill in this continuum with compatible edos, increasing in number of tones as we continue filling in the in-betweens. Thus, the smallest in-between edo would be (3+2)\(10+7) = 5\17 -- five degrees of [[17edo|17edo]]: | The generator range reflects two extremes: one where L=s (3\10), and another where s=0 (2\7). Between these extremes, there is an infinite continuum of possible generator sizes. By taking freshman sums of the two edges (adding the numerators, then adding the denominators), we can fill in this continuum with compatible edos, increasing in number of tones as we continue filling in the in-betweens. Thus, the smallest in-between edo would be (3+2)\(10+7) = 5\17 -- five degrees of [[17edo|17edo]]: | ||
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You can also build this scale by stacking neutral thirds that are not members of edos -- for instance, frequency ratios 11:9, 49:40, 27:22, 16:13 -- or the square root of 3:2 (a bisected just perfect fifth). | You can also build this scale by stacking neutral thirds that are not members of edos -- for instance, frequency ratios 11:9, 49:40, 27:22, 16:13 -- or the square root of 3:2 (a bisected just perfect fifth). | ||
= Rank-2 temperaments = | == Rank-2 temperaments == | ||
=7-note subsets= | ==7-note subsets== | ||
If you stop the chain at 7 tones, you have a heptatonic scale of the form [[3L_4s|3L 4s]]: | If you stop the chain at 7 tones, you have a heptatonic scale of the form [[3L_4s|3L 4s]]: | ||